A Virgin Atlantic spokeswoman said: "The allegations that have been raised are extremely serious and we have launched an immediate investigation.

"The security of customer information is our highest priority and we have robust processes in place to ensure that passenger information is protected.

"The incident that has been alleged concerns eight customers' flights booked in 2010 and we are in contact with all of those people.

"It is too early to draw conclusions on this matter but of course we would deeply regret any concern that these allegations may cause the individuals involved."

A source at the airline Sir Richard Branson launched in 1984 said it was scanning through email archives and investigating who could access its booking system. The accused employee, who held a relatively junior position, denies the allegations, it is understood.

A spokeswoman for Defoe said: "This is a serious breach of privacy. We'll be consulting with our lawyers and investigating the matter further."

A spokeswoman for Miller, who obtained an injunction against the paparazzi in 2008, said she had no comment to make. The actress has previously given evidence to the Leveson Inquiry into press standards, describing the intrusion she said she suffered at the hands of photographers.